Whenever we hurt or affend another, it is so easy to not want to be seen as the guilty party. We may say something like, "I'm sorry for hurting you, BUT, I didn't hit you that hard OR, the offense that I did to you wasn't that bad. YOU are making a big do about nothing." Often this is subtle attempt to get the blame off of us and to transfer at least part of the blame to the other party.
As a parent, one thing that I am learning, is when I apologize, I only focus on what I did that was wrong. Even if the other party was (in my mind) as much or more to blame than myself, I only confess to what I did, without mentioning anything at all about what I think that the other person did.
An apology or a confession that says or implies, even to the smallest degree, that someone else is partly or largely to blame is a hollow confession. It is our subtle attempt to get the focus off of us and onto the other party.
Our confession is about our own inner cleansing. It is about taking full responsibility for our own behavior. It is also deeply connected with our practice of humility.
If someone else has offended us, that should be dealt with at a different time. Whenever someone has offended or hurt us, we need to deal with it promptly so that their offence doesn't get intertwined with our own behavior later on.
Any time that we even remotely involved in or associated with an argument or disagreement, we need to step aside and examine our own thoughts, motives and actions. For example, recently my two children were involved in fight of sorts. I went out to take care of it. After letting them both tell me both sides, I was overly zealous to correct the one I thought was at greater fault. The child I was correcting and I both were at odds with each other. It was only after I had stepped away from it and went for a walk that I realized that I was at fault for the way I had handled the child. I could have made an excuse that the child was really at fault. But I knew that I had to set the example. I took time to examine what I had done wrong. Then, when I got back home, I told the child, "My behavior was wrong. I was too harsh and judgemental when I spoke to you earlier...." After I had finished apologizing, my child also apologized to me as well. I'd had that happen a number of times. It seems that I have to be the one to apologize first, then the other person will often also apologize also.